Finite Group Databasebeta

← #29697017

Subgroups — #29697017

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839820C211yesmaximal, characteristic, complemented
2#21448202C211yesmaximal, characteristic
3#21446435C211yesmaximal, characteristic, complemented
4#21446429C211yesmaximal, characteristic, complemented
5#21446428C211yesmaximal, characteristic, complemented
6#21446422C211yesmaximal, characteristic, complemented
7#21446002C211yesmaximal, characteristic, complemented
8#21446002C211yesmaximal, characteristic, complemented
9#21445888C211yesmaximal, characteristic, complemented
10#21445801C211yesmaximal, characteristic, complemented
11#21445729C211yesmaximal, characteristic
12#21445600C211yesmaximal, characteristic, complemented
13#21445600C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C2×C61×#407C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18#16839820—24no—
19C2×#14519706C2211yescharacteristic, complemented
20C2×#14519706C2211yescharacteristic, complemented
21C2×#14519706C2211yescharacteristic, complemented
22C2×#14519706C2211yescharacteristic, complemented
23C2×C22⋊#92418C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519687C2211yescharacteristic, complemented
30C2×#14519687C2211yescharacteristic, complemented
31C2×C8×Dic61C2211yescharacteristic, complemented
32C2×C8×Dic61C2211yescharacteristic, complemented
33#16839625C411yescharacteristic
34#16839625C411yescharacteristic
35#16839622C411yescharacteristic
36#16839622C411yescharacteristic
37#16839622C411yescharacteristic
38#16839622C411yescharacteristic
39#16839618C411yescharacteristic
40#16839618C411yescharacteristic
41C4×C22⋊Dic61C2211yescharacteristic
42C4×C22⋊Dic61C2211yescharacteristic
43C4×C22⋊Dic61C2211yescharacteristic
44C4×C22⋊Dic61C2211yescharacteristic
45#16839516C2211yescharacteristic, complemented
46#16839516C2211yescharacteristic, complemented
47#16839516C2211yescharacteristic, complemented
48#16839516C2211yescharacteristic, complemented
49#16839516C2211yescharacteristic, complemented
50#16839516C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C24×C4×C61C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C61×#407—24no—
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519736—22no—
66#14519736—22no—
67#14519736—41no—
68#14519736—41no—
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×C4⋊Dic61C2×C411yescharacteristic
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×C22⋊Dic61C2×C411yescharacteristic
74C2×C22⋊Dic61C2×C411yescharacteristic
75C2×C22⋊Dic61C2×C411yescharacteristic
76C2×C22⋊Dic61C2×C411yescharacteristic
77C2×C22⋊Dic61C2×C411yescharacteristic
78C2×C22⋊Dic61C2×C411yescharacteristic
79C2×C22⋊Dic61C2×C411yescharacteristic
80C2×C22⋊Dic61C2×C411yescharacteristic
81C2×C22⋊Dic61C2×C411yescharacteristic
82C2×C22⋊Dic61C2×C411yescharacteristic
83C2×C22⋊Dic61C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#14519706—22no—
90#14519706—22no—
91#14519706—41no—
92#14519706—41no—
93C22⋊#92418—22no—
94C22⋊#92418—22no—
95C22⋊#92418—22no—
96C22⋊#92418—22no—
97C22⋊#92418—41no—
98C22⋊#92418—41no—
99#14519687—22no—
100#14519687—41no—
101C8×Dic61—22no—
102C8×Dic61—41no—
103#14519684C2×C411yescharacteristic
104#14519684C2×C411yescharacteristic
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111C25×C61C2×C411yescharacteristic
112C23×C4×C61—22no—
113C23×C4×C61—22no—
114C23×C4×C61—22no—
115C23×C4×C61—22no—
116C23×C4×C61—41no—
117C23×C4×C61—41no—
118C23×C4×C61C2×C411yescharacteristic
119C23×C4×C61C2×C411yescharacteristic
120C23×C4×C61C2×C411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C2×M16×C61—22no—
125C2×M16×C61—22no—
126C2×M16×C61—22no—
127C2×M16×C61—22no—
128C2×M16×C61—41no—
129C2×M16×C61—41no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22⋊C8×C61—22no—
135C22⋊C8×C61—22no—
136C22⋊C8×C61—22no—
137C22⋊C8×C61D414yes—
138C24×C61—22no—
139C24×C61—22no—
140C24×C61—22no—
141C24×C61—41no—
142C24×C61—41no—
143C24×C61—41no—
144C24×C61—41no—
145C24×C61C22×C411yescharacteristic
146C24×C61C22×C411yescharacteristic
147C24×C61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—41no—
169C22×C4×C61—41no—
170C22×C4×C61—41no—
171C22×C4×C61—44no—
172C22×C4×C61—44no—
173C22×C4×C61—44no—
174C22×C4×C61—44no—
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C22×C4×C61C2×D412yes—
179C22×C4×C61#4112yes—
180C22×C4×C61#4112yes—
181C22×C4×C61#4112yes—
182C22×C4×C61C2411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191M16×C61—44no—
192M16×C61—44no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61C2×D412yes—
204C2×C8×C61C2×D412yes—
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—41no—
210C22⋊Dic61—41no—
211C22⋊Dic61—41no—
212C22⋊Dic61—41no—
213C22⋊Dic61—41no—
214C22⋊Dic61—41no—
215C22⋊Dic61—41no—
216C22⋊Dic61—41no—
217C4⋊Dic61—22no—
218C4⋊Dic61—22no—
219C4⋊Dic61—41no—
220C4⋊Dic61—41no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—44no—
260C23×C61—44no—
261C23×C61—44no—
262C23×C61—44no—
263C23×C61—44no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61#11712yes—
267C23×C61C4×D412yes—
268C23×C61#13112yes—
269C23×C61C23×C411yescharacteristic
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—44no—
286C2×C4×C61—44no—
287C2×C4×C61—44no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61#11712yes—
293C2×C4×C61C4×D412yes—
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C8×C61—22no—
325C8×C61—22no—
326C8×C61—41no—
327C8×C61—41no—
328#92418—41no—
329#92418—41no—
330#92418—41no—
331#92418—41no—
332#22559—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—416no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61C2×#11711yescharacteristic
356C22×C61C2×C4×D411yescharacteristic
357C22×C61#51811yescharacteristic
358C22×C61C2×#13111yescharacteristic
359C22×C61#56811yescharacteristic
360C22×C61#56811yescharacteristic
361C22×C61#56811yescharacteristic
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—41no—
365C4×C61#54611yescharacteristic
366C4×C61#54611yescharacteristic
367C4×C61#55111yescharacteristic
368C4×C61#55111yescharacteristic
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61—41no—
373Dic61—41no—
374Dic61—41no—
375Dic61—41no—
376Dic61—41no—
377C2×#433—611no—
378C2×#407D6111yescharacteristic
379#2280—611no—
380#1924—611no—
381#1924—611no—
382#1923—611no—
383#1923—611no—
384#1851—611no—
385#1851—611no—
386#1818—611no—
387#1798—611no—
388#1779—611no—
389#1753—611no—
390#1753—611no—
391#1750—611no—
392C2×C61—42no—
393C2×C61—42no—
394C2×C61—42no—
395C2×C61#234211yescharacteristic
396C2×C61#292111yescharacteristic
397C2×C61#292411yescharacteristic
398C2×C61#293011yescharacteristic
399C2×C61#293311yescharacteristic
400C2×C61#297611yescharacteristic
401C2×C61#297811yescharacteristic
402C24×C4C2×D6111yescharacteristic
403C22×M16C2×D6111yescharacteristic
404C22×M16C2×D6111yescharacteristic
405C2×#117—611no—
406C2×#117—611no—
407#433—1224no—
408C2×C4⋊C8—611no—
409C2×C4⋊C8—611no—
410C2×C4⋊C8—611no—
411C2×C4⋊C8—611no—
412#407—24no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419C2×C22⋊C8C2×D6111yescharacteristic
420C2×C22⋊C8C2×D6111yescharacteristic
421C2×C22⋊C8C2×D6111yescharacteristic
422C2×C22⋊C8C2×D6111yescharacteristic
423C2×#97—611no—
424C2×#97—611no—
425C2×C4×C8—611no—
426C2×C4×C8—611no—
427#381—611no—
428#381—611no—
429#380—611no—
430#380—611no—
431#380—611no—
432#380—611no—
433#379—611no—
434#379—611no—
435C4×C22⋊C4—611no—
436C4×C22⋊C4—611no—
437C4×C22⋊C4—611no—
438C4×C22⋊C4—611no—
439#336—611no—
440#336—611no—
441#336—611no—
442#336—611no—
443#336—611no—
444#336—611no—
445#336—611no—
446#336—611no—
447C61#2255911yescharacteristic, complemented, Sylow
448C25C4×D6111yescharacteristic
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4C4×D6111yescharacteristic
456C23×C4C4×D6111yescharacteristic
457C23×C4C4×D6111yescharacteristic
458C23×C4C22×D6111yescharacteristic
459C23×C4C22×D6111yescharacteristic
460C23×C4C22×D6111yescharacteristic
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—41no—
466C2×M16—41no—
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8C22×D6111yescharacteristic
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475#117—1222no—
476#117—1222no—
477#117—2441no—
478#117—2441no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—611no—
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C4⋊C8—2441no—
502C4⋊C8—2441no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—1222no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—1222no—
510C22⋊C8—2441no—
511C22⋊C8—2441no—
512C22⋊C8C22⋊D6114yes—
513#97—1222no—
514#97—2441no—
515C4×C8—1222no—
516C4×C8—2441no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95—611no—
522#95—611no—
523#95—611no—
524#95—611no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24C2×C4×D6111yescharacteristic
533C24C2×C4×D6111yescharacteristic
534C24C2×C4×D6111yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4C2×C4×D6111yescharacteristic
571C22×C4C2×C4×D6111yescharacteristic
572C22×C4C2×C4×D6111yescharacteristic
573C22×C4#1175822212yes—
574C22×C4#1175822412yes—
575C22×C4#1175822412yes—
576C22×C4C2×C22⋊D6112yes—
577C22×C4C23×D6111yescharacteristic
578M16—44no—
579M16—44no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8C2×C22⋊D6112yes—
603C2×C8C2×C22⋊D6112yes—
604C4⋊C4—1222no—
605C4⋊C4—1222no—
606C4⋊C4—2441no—
607C4⋊C4—2441no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—2441no—
613C22⋊C4—2441no—
614C22⋊C4—2441no—
615C22⋊C4—2441no—
616C22⋊C4—2441no—
617C22⋊C4—2441no—
618C22⋊C4—2441no—
619C22⋊C4—2441no—
620C42—1221no—
621C42—1221no—
622C42—1221no—
623C42—1221no—
624C42—1221no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#1451973312yes—
654C23C4×C22⋊D6112yes—
655C23#1451978512yes—
656C23C22×C4×D6111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4#1451973312yes—
704C2×C4C4×C22⋊D6112yes—
705C2×C4C22×C22⋊D6111yescharacteristic
706C2×C4C2×#1175822411yescharacteristic
707C2×C4C2×#1175822411yescharacteristic
708C2×C4C2×#1175822211yescharacteristic
709C2×C4#1451982211yescharacteristic
710C2×C4#1451982211yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—2441no—
716C8—2441no—
717C8—2441no—
718C8—2441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—416no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22C2×#1451973311yescharacteristic
742C22C2×C4×C22⋊D6111yescharacteristic
743C22#1684023511yescharacteristic
744C22C2×#1451978511yescharacteristic
745C22#1684052811yescharacteristic
746C22#1684052811yescharacteristic
747C22#1684052811yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—2441no—
752C4—2441no—
753C4—2441no—
754C4—2441no—
755C4—2441no—
756C4—2441no—
757C4—2441no—
758C4—2441no—
759C4#1684040611yescharacteristic
760C4#1684040611yescharacteristic
761C4#1684043811yescharacteristic
762C4#1684043811yescharacteristic
763C2—42no—
764C2—42no—
765C2—42no—
766C2#2144866411yescharacteristic
767C2#2145445411yescharacteristic
768C2#2145447911yescharacteristic
769C2#2145452211yescharacteristic
770C2#2145454411yescharacteristic
771C2#2145486911yescharacteristic
772C2#2145487911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#407C2
prime radicalC25×C61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×#407D61
hypocenterC61#22559
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16839820C2semidirect
3. #21446435C2semidirect
4. #21446429C2semidirect
5. #21446428C2semidirect
6. #21446422C2semidirect
7. #21446002C2semidirect
8. #21446002C2semidirect
9. #21445888C2semidirect
10. #21445801C2semidirect
12. #21445600C2semidirect
13. #21445600C2semidirect
14. #21445587C2semidirect
19. C2×#14519706C22semidirect
20. C2×#14519706C22semidirect
21. C2×#14519706C22semidirect
22. C2×#14519706C22semidirect
29. C2×#14519687C22semidirect
30. C2×#14519687C22semidirect
31. C2×C8×Dic61C22semidirect
32. C2×C8×Dic61C22semidirect
45. #16839516C22semidirect
46. #16839516C22semidirect
47. #16839516C22semidirect
48. #16839516C22semidirect
49. #16839516C22semidirect
50. #16839516C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
447. C61#22559semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168398202
#214482022
#214464352
#214464292
#214464282
#214464222
#214460022
#214458882
#214458012
#214457292
#214456002
#214455872
C2×C61×#4072
#2255961